How to prove this exponential inequality? – math.stackexchange.com

Let $x,y,z\in\mathbb R$. Prove that $\displaystyle \frac{2^{10x}}{2^y+2^z} +\frac{2^{10y}}{2^z+2^x} +\frac{2^{10z}}{2^x+2^y} \ge 2^{6x+2y+z-1} +2^{6y+2z+x-1} +2^{6z+2x+y-1}.$

Set $ a=2^x, ...